For the CBC signals detected by ground-based detectors like LIGO and Virgo,
a Bayesian model selection method has been used by comparing the assumptions of
the GW is constitute of pure vector or tensor mode against pure tensor mode,
and the obtained results still prefer the pure tensor mode assumption [1]}, [2]}, [3]}.
For the sources detected by at least three detectors,
the null-stream method [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]} can be used to test if there exist non-tensor mode.
This method has been used for the O2, O3a and O3b GW events [11]}, [12]},
but the data is still consistent with the pure tensor mode hypothesis and other polarization hypotheses beyond GR are relatively disfavored.
However, with three detectors, we can only determine the existence of non-tensor modes [13]}, [14]}.
In order to distinguish the extra modes, we need a network with more detectors to get enough degree of freedom.
